Is there a word or rhetorical device for when a statement and its opposite are both true at the same time?

I think you are looking for the rhetorical device called antiphrasis:

a literary device which uses word or phrase to convey the opposite sense of their real meanings. As a figure of speech the word or phrase is used in a way that is completely opposite to its literal meaning which creates either irony or a comic effect in the sentence.

It might be antithesis, dialetheism or dichotomy.

Antithesis:

In rhetoric, antithesis is a figure of speech involving the bringing out of a contrast in the ideas by an obvious contrast in the words, clauses, or sentences, within a parallel grammatical structure.

[Wikipedia]

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Dialetheism:

Dialetheism (from Greek δι- di- 'twice' and ἀλήθεια alḗtheia 'truth') is the view that there are statements which are both true and false. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called "true contradictions", dialetheia, or nondualisms.

[Wikipedia]

You have described a paradox fairly well.

A paradox is a statement that contradicts itself, or that must be both true and untrue at the same time. Paradoxes are quirks in logic that demonstrate how our thinking sometimes goes haywire, even when we use perfectly logical reasoning to get there.

Here is a particularly difficult paradox to decipher, particularly if you are not familiar with biblical, theological issues. Said Jesus Christ,

“If anyone wishes to come after Me, he must deny himself, and take up his cross and follow Me. For whoever wishes to save his life will lose it; but whoever loses his life for My sake will find it. For what will it profit a man if he gains the whole world and forfeits his soul? Or what will a man give in exchange for his soul?" (Matthew 16:24-26, my bolding)

An interlocutor who might wish to take exception to what Jesus said, might say the following:

I'm not picking up what you're laying down, Jesus. I have no intention of being crucified. Quite the opposite, in fact. I intend to live my life to the full by choosing not to walk in your footsteps. I have no intention of giving my life to you and your cause!"

To the statement, Jesus might respond by saying,

My friend, the only way you can live your life to the full is to do so in the way I've laid out for you. That way may involve some pain, hardship, suffering, and sacrifice, but the reward in eternity will far exceed the greatest joy you believe you can experience on earth by not taking my way. Hey, would you agree to have all the riches the world can offer, but only if you agreed to forfeit your life? I don't think so.

According to Wittgenstein and many others, "Contradictions do not exist." You can resolve the apparent contradiction in your question by considering the points of view involved, as noted by @Stockfish.

First, the exceptional performer's team members believe she is making them look bad by virtue of her stellar efforts. They are assuming that "the boss" can see what's happening within the team -- who is contributing what. They may or may not be correct. If they are correct, she is in fact making them look bad, but they are not necessarily correct.

Second, the exceptional performer believes that she is making her teammates look good by virtue of her efforts. She is assuming that "the boss" sees only the performance of the team -- not who is contributing what. She may or may not be correct. If she is correct, she is in fact making them look good, but she is not necessarily correct.

In any event, there is no contradiction, only the fact that the exceptional performer and the other team members are expressing different points of view based on different assumptions. Only the boss knows which of the two different perspectives is correct.

Like some of the other answers, I agree that your examples do not quite match the question. It sounds to me like you are referring to the 'Liars Paradox'. Modified to match your example, it would read like so:

The following statement is true.
The preceding statement is false.

Plato.Stanford on the Subject

If being true includes all cases of “I don't know”, then this is called: a statement cannot be falsified.

Here, we do not know whether the external observer is looking at the team as a whole or evaluating the performance of each team member individually, and as long as we consider both to be possible, both statements can be true.

If a statement is not falsifiable, it is no longer evidence but a question of belief. Hence, any scientific proof isn’t to prove that an assumption is true, but that the opposite (or any other solution, if there are several possibilities) must be wrong.

I would say that

"you’re making the rest of us look bad” because of how well they are performing, and the coworker replies “actually, I’m making the rest of you look good”

might be an instance of spinning as intended in Spin (propaganda) in Wikipedia:

A standard tactic used in "spinning" is to reframe or modify the perception of an issue or event to reduce any negative impact it might have on public opinion.

However, I do acknowledge that your example does not necessarily imply the manipulative efforts that is understated in propaganda.

More neutrally, I would simply call it another point of view or relativization. I ignore whether this intent needs to have grown into a fully-fledged rhetorical device.

My two cents. Not a mother-tongue speaker.

Contradiction. According to Aristotle, this leads to everything being true. But the word true implies that its negation exists and is negated. Truth is a fundamentally negative concept. It only makes sense if it excludes its opposite. In your example, this is expressed by the word "actually". My point is: this is impossible and thus just indicates a sloppy logic.